RMS-to-DC converters are electronic circuits that generate a DC output signal (either current or voltage), proportional to the Root-Mean-Square value (the square-root of the power) of the input signal. Such devices are used in a variety of applications where a measure of the signal strength is important, such as test and measurement and communications. A specific property of devices that produce an output based on the RMS value of the input (the relationship between RMS input value and DC output is not necessarily linear, but can also be quadratic, logarithmic or another nonlinear function) is that their response is insensitive to the precise shape of the input signal; more specifically, it is insensitive to peak-to-average power ratio variations. This is especially important in applications were the converter input signals can attain multiple different formats (modulation parameters, variable coding, etc.) and thus different peak-to-average power ratios. In such systems, signal strength measurement using an RMS-to-DC converter significantly reduces the need for factory calibration.
The two key operations to be implemented by any RMS-to-DC converter are squaring of the input signal, and low-pass filtering of the resulting squared signal. In addition, other functions like taking the square-root (to create a linear RMS-DC conversion) or logarithm (for LOG-RMS-DC conversion) of this means-square value can be included to change the overall input-output relationship according to needs. In order to maximize the performance of the converter, the aforementioned operations should be realized in such a way that circuit imperfections such as offset, temperature drift, etc. have a minimal impact on the converter overall transfer.
Direct RMS-to-DC Conversion
The most straight-forward method of implementing an RMS-to-DC converter, direct RMS-to-DC conversion, is to apply all required operations sequentially, as illustrated by device 100 of FIG. 1. First, the input signal x is squared 110, then low-pass filtered 120, and finally the square-root operation 130 is applied. The overall transfer of this converter can be expressed as:
                              y          =                                    K              sqrt                        ⁢                                                                                K                    sq                                    ⁢                                      x                    2                                                  _                                                    ,                            (        1        )            and is thus dependent on both the conversion gain from input x to output y of squarer 110, Ksq, and the conversion gain of square-root circuit 130, Ksqrt. Both conversion gains are highly dependent on transistor device characteristics, and therefore are subject to temperature drift, frequency dependence, and other sources of inaccuracy. Since the signal of interest at the output of the squarer is situated at DC (zero frequency), offsets adding to the circuit at locations x1 and x2 in FIG. 1 significantly limit the sensitivity of the converter for small input signals. This is illustrated by graph 200 of FIG. 2. The dashed ideal offset-free RMS-to-DC converter transfer maintains its sensitivity down to a zero input signal level, while a practical converter, impaired by internal offsets, is usable only down to an input signal level xmin. Reduction of internal offsets will therefore extend the converter dynamic range.RMS-to-DC Conversion Based on the Difference of Squares
FIG. 3 illustrates one device 300 of RMS-to-DC conversion that eliminates the conversion gain of the squarer and square-root circuit from the overall converter transfer. The method employed by device 300 is also known as RMS-to-DC conversion based on the “difference of squares.” In this configuration, a linear analog multiplier 310 is used to generate the difference of the square of the input signal (x) and the square of the output signal (y), i.e. x2−y2. This is achieved by supplying one multiplier input with the sum of the input signal and the output signal, and the other input with the difference of these signals. The resulting difference of squares is fed through lowpass filter 320 and supplied to a high-gain error amplifier 330. When the gain A of the amplifier 330 approaches infinity, the output signal y becomes proportional to the RMS value of the input signal x. This can be seen as follows. Starting at the output and following the feedback backwards through the multiplier, the relation between input signal x and output signal y can be expressed as:y=AKm└ x2−β1β2 y2+(β1−β2) xy┘  (2)
Since the output signal is DC, the mean value of y equals y itself, and the mean-square value equals the square of y. Furthermore, since the input signal x for useful RMS-to-DC converter applications is zero-mean, the last term on the right of Equation 2 vanishes (this also occurs independent of x when β1=β2), and y becomes:
                    y        =                                            -              1                                      2              ⁢                              AK                m                            ⁢                              β                1                            ⁢                              β                2                                              +                                                    1                                                      (                                          2                      ⁢                                              AK                        m                                            ⁢                                              β                        1                                            ⁢                                              β                        2                                                              )                                    2                                            +                                                                    x                    2                                    _                                                                      β                    1                                    ⁢                                      β                    2                                                                                                          (        3        )            which approaches the following expression for high error amplifier gain levels:
                                          lim                          A              →              ∞                                ⁢                      y                                                                =                                                            x                2                            _                                                      β                1                            ⁢                              β                2                                                                        (        4        )            Consequently, for high loopgain levels, the overall RMS-to-DC converter transfer is independent of the multiplier conversion gain Km, and only determined by the (low-frequency) feedback factors β1 and β2. These can be accurately realized, for example, by passive components. Offset though, especially offset adding to the input and output of the multiplier, can still significantly limit the sensitivity of this type of converter for small input signal levels.
FIG. 4 illustrates another device 400 for generating the difference of squares using two squaring circuits 410 and 420. Again, the amplifier 440 in the loop drives the difference between the mean-square value of the input signal and the squared output signal to zero, such that the output signal approaches:
                                          lim                          A              →              ∞                                ⁢                      y                                                                =                                                            K                                  sq                  ⁢                                                                          ⁢                  1                                                            K                                  sq                  ⁢                                                                          ⁢                  2                                                      ⁢                                          x                2                            _                                                          (        5        )            Thus in this approach, the accuracy of the overall converter transfer is based on matching between the conversion gain of the two squaring circuits 410 and 420, instead of the squarer conversion gain itself. Offset, especially offset adding to the squarer output signals, still affects the sensitivity at low input signal levels. Therefore, careful IC layout and trimming are required to maximize the converter dynamic range.